Frequency Response of Parametric Resonance of Electrostatically Actuated Bio-MEMS Circular Membranes

This paper deals with the amplitude-frequency response of parametric resonance of electrostatically actuated Bio-MEMS circular membrane resonators. The system consists of a flexible clamped circular membrane over a parallel fixed ground plate. Between the membrane and the ground plate is an alternating current (AC) voltage. The magnitude of the AC voltage is in the range of soft excitation. The AC frequency used to actuate the Bio-MEMS is near the first natural frequency of the membrane. Since the electrostatic force is proportional to the square of the voltage, this actuation leads to parametric resonance of Bio-MEMS circular membranes. The equation of motion includes Casimir and Van deer Waals forces. Two methods of investigation are utilized in this paper, the method of multiple scales (MMS), and the reduced order model (ROM). They are used to analytically and numerically solve the differential equations of motion for amplitude-frequency response of Bio-MEMS membrane resonators. The effects of Casimir force, Van der Waals force, voltage, and damping on the amplitude-frequency response of the system are also reported. The results show that the increase of Casimir and Van der Waals parameters increase the softening effect of the response, i.e., the response shifts towards lower frequencies and amplitudes. The results also showed that an increase in the damping parameter decreased the escape band of the response, while increasing the voltage parameter had the opposite effect increasing the size of the escape band.